%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : COL044-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:08:59 PM UTC 2026
% Result : Unsatisfiable 8.21s 11.57s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL044-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.44 % Computer : n008.cluster.edu
% 0.15/10.44 % Model : x86_64 x86_64
% 0.15/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.44 % Memory : 8046.5625MB
% 0.15/10.44 % OS : Linux 6.8.0-71-generic
% 0.15/10.44 % CPULimit : 300
% 0.15/10.44 % WCLimit : 300
% 0.15/10.44 % DateTime : Mon Sep 21 14:07:35 UTC 2026
% 0.15/10.44 % CPUTime :
% 0.15/10.45 % Drodi V4.1.1
% 8.21/11.57 % Refutation found
% 8.21/11.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.21/11.57 % SZS output start CNFRefutation for theBenchmark
% 8.21/11.57 fof(f1,axiom,(
% 8.21/11.57 (![X,Y,Z]: (apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ))),
% 8.21/11.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.21/11.57 fof(f2,axiom,(
% 8.21/11.57 (![X,Y,Z]: (apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z) ))),
% 8.21/11.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.21/11.57 fof(f3,axiom,(
% 8.21/11.57 (![Strong_fixed_point]: (( apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt))| fixed_point(Strong_fixed_point) ) ))),
% 8.21/11.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.21/11.57 fof(f4,negated_conjecture,(
% 8.21/11.57 ~ fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b)) ),
% 8.21/11.57 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 8.21/11.57 fof(f5,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(b,X0),X1),X2)=apply(X0,apply(X1,X2)))),
% 8.21/11.57 inference(cnf_transformation,[status(thm)],[f1])).
% 8.21/11.57 fof(f6,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(n,X0),X1),X2)=apply(apply(apply(X0,X2),X1),X2))),
% 8.21/11.57 inference(cnf_transformation,[status(thm)],[f2])).
% 8.21/11.57 fof(f7,plain,(
% 8.21/11.57 ![X0]: (~apply(X0,fixed_pt)=apply(fixed_pt,apply(X0,fixed_pt))|fixed_point(X0))),
% 8.21/11.57 inference(cnf_transformation,[status(thm)],[f3])).
% 8.21/11.57 fof(f8,plain,(
% 8.21/11.57 ~fixed_point(apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b)),b))),
% 8.21/11.57 inference(cnf_transformation,[status(thm)],[f4])).
% 8.21/11.57 fof(f9,plain,(
% 8.21/11.57 ![X0,X1]: (~apply(apply(apply(b,X0),X1),fixed_pt)=apply(fixed_pt,apply(X0,apply(X1,fixed_pt)))|fixed_point(apply(apply(b,X0),X1)))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f5,f7])).
% 8.21/11.57 fof(f10,plain,(
% 8.21/11.57 ![X0,X1]: (~apply(X0,apply(X1,fixed_pt))=apply(fixed_pt,apply(X0,apply(X1,fixed_pt)))|fixed_point(apply(apply(b,X0),X1)))),
% 8.21/11.57 inference(forward_demodulation,[status(thm)],[f5,f9])).
% 8.21/11.57 fof(f17,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,X0)),X1),X2)=apply(apply(X0,apply(X2,X1)),X2))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f5,f6])).
% 8.21/11.57 fof(f20,plain,(
% 8.21/11.57 ![X0,X1,X2,X3]: (apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3)=apply(apply(apply(X0,apply(X1,X3)),X2),X3))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f5,f6])).
% 8.21/11.57 fof(f25,plain,(
% 8.21/11.57 ~apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b),apply(b,fixed_pt))=apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b),apply(b,fixed_pt)))),
% 8.21/11.57 inference(resolution,[status(thm)],[f10,f8])).
% 8.21/11.57 fof(f26,plain,(
% 8.21/11.57 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n)),b),apply(b,fixed_pt)))),
% 8.21/11.57 inference(forward_demodulation,[status(thm)],[f5,f25])).
% 8.21/11.57 fof(f27,plain,(
% 8.21/11.57 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt))))),
% 8.21/11.57 inference(forward_demodulation,[status(thm)],[f5,f26])).
% 8.21/11.57 fof(f76,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2)=apply(X0,apply(apply(X2,X1),X2)))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f5,f17])).
% 8.21/11.57 fof(f109,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(apply(n,apply(b,b)),X0),X1),X2)=apply(apply(X1,X0),apply(X1,X2)))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f17,f5])).
% 8.21/11.57 fof(f398,plain,(
% 8.21/11.57 ![X0,X1,X2]: (apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2)=apply(apply(X0,X2),apply(X1,X2)))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f5,f20])).
% 8.21/11.57 fof(f1034,plain,(
% 8.21/11.57 ![X0,X1]: (apply(apply(apply(n,apply(n,apply(b,b))),X0),X1)=apply(apply(X0,X1),apply(X0,X1)))),
% 8.21/11.57 inference(paramodulation,[status(thm)],[f6,f109])).
% 8.21/11.57 fof(f1746,plain,(
% 8.21/11.57 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 8.21/11.58 inference(paramodulation,[status(thm)],[f398,f27])).
% 8.21/11.58 fof(f4646,plain,(
% 8.21/11.58 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))=apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))))),
% 8.21/11.58 inference(paramodulation,[status(thm)],[f1034,f1746])).
% 8.21/11.58 fof(f5605,plain,(
% 8.21/11.58 ~apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(n,apply(b,b))),n))),n),apply(b,apply(b,fixed_pt)))=apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))),
% 8.21/11.58 inference(paramodulation,[status(thm)],[f76,f4646])).
% 8.21/11.58 fof(f5606,plain,(
% 8.21/11.58 ~apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))=apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))),
% 8.21/11.58 inference(paramodulation,[status(thm)],[f398,f5605])).
% 8.21/11.58 fof(f5607,plain,(
% 8.21/11.58 ~apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))=apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))),
% 8.21/11.58 inference(paramodulation,[status(thm)],[f1034,f5606])).
% 8.21/11.58 fof(f5608,plain,(
% 8.21/11.58 $false),
% 8.21/11.58 inference(trivial_equality_resolution,[status(thm)],[f5607])).
% 8.21/11.58 % SZS output end CNFRefutation for theBenchmark.p
% 3.12/11.60 % Elapsed time: 1.147722 seconds
% 3.12/11.60 % CPU time: 8.916704 seconds
% 3.12/11.60 % Total memory used: 169.176 MB
% 3.12/11.60 % Net memory used: 167.186 MB
%------------------------------------------------------------------------------